European patent application No. 0801305 describes an apparatus for characterizing a suspension. The apparatus generates ultrasonic pulses in a beam in a liquid. Reflection of a pulse on an individual particle in the liquid results in an echo. If the particle is at a given position, the amplitude of the reflection is coupled one-to-one to the size of the particle. Accordingly, in measurements on reflections of consecutive pulses on particles of different sizes, different amplitudes are measured.
The known apparatus makes a histogram of counts of the number of times that reflections of different amplitudes occur. The histogram contains information about the particle size distribution, that is, the concentration of particles as a function of the size of the particles. With information about the particle size distribution, in turn, for instance the total concentration of particles in the liquid can be determined.
European patent application No. 0801305 describes a technique to extract information about the size from the distribution of the amplitudes. An expression is used for the probability that reflections of different amplitudes occur. This expression relates the probability to the particle size distribution. If the reflecting particles were always at the same place in the beam, the number of reflections having a particular amplitude would be proportional to the fraction of particles having the size leading to that amplitude.
However, the information about the particle size distribution is smeared across the amplitudes because the reflection amplitude of a particle, besides being dependent on the size of the particle, also depends on the position of the particle in the beam. The farther the particle is off the center of the beam at reflection, the smaller the amplitude. The expression used for the probability of a reflection measurement with a particular amplitude smears the particle size distribution across the amplitude distribution to give expression to this effect.
Using a maximum likelihood technique, parameters of the particle size distribution are estimated that maximize the thus expressed probability of the actually measured numbers of particles. Thus, smearing is undone. In the concrete, the parameters are chosen such that a sum is minimized of the squares of the differences between measured numbers of reflections with amplitudes in different amplitude ranges and predicted numbers. Such a sum is an indication for the probability of the combination of measured reflections, but of course also other indications of the probability can be used, such as the product of the probabilities of the different measured amplitudes.
A prerequisite for the technique used is that the reflections of individual particles can be distinguished. If reflections of several particles are measured indiscriminately, a part of the reflections will be masked. Thus, reflection of a larger particle can make reflection of a smaller particle invisible, but reflection of a smaller particle can also mask reflection of a larger particle if the larger particle is sufficiently much farther from the center of the beam than is the smaller particle.
Accordingly, the technique gives reliable results only when concentrations are sufficiently low. The maximum usable concentration can be raised by minimizing the volume in which particles are indistinguishably measured, for instance by the use of a focused beam and small time windows in which echoes are accepted. However, there are limits to the applicability of such techniques. That is why the requirement of separate observation of individual particles limits the applicability of the technique.